In MRI, a separation imaging method is exemplified where chemical shift, i.e., deviation of the resonant frequency of the same type of nucleus due to difference in molecular structure of two components, is utilized, and the same tomography surface in a human body is indicated in separation into a proton image of water only and a proton image of fat only.
First, Dickson method in the prior art being one of the separation imaging method of water and fat will be described referring to FIGS. 4, 5A and 5B. FIG. 4 is a diagram representing pulse sequence of Dickson method in the prior art. In FIG. 4, t is time axis and the applying timing of 90.degree. pulse is made t=0. In the hereinafter description, the static magnetic field direction (being horizontal) is made Z axis, the vertical direction is made Y axis, and the horizontal direction (right-hand system) perpendicular to the Z axis is made X axis. RF designates a RF (Radio-Frequency) wave of Lamour frequency for rotating the magnetization vector of proton directed in the Z-axis direction by prescribed angle in the direction perpendicular thereto, which is called 90.degree. pulse or 180.degree. pulse depending on the rotational angle. SE designates a spin echo signal observed in that 90.degree. pulse in t=0 is applied and then phase of the magnetization vector dispersed in the XY plane due to unevenness of the static magnetic field is inverted by 180.degree. pulse and converged again. Time from 90.degree. pulse until obtaining the spin echo is made T.sub.E. In Dickson method, at first, S.sub.0 scan is performed in the applying timing of 180.degree. pulse mode t=T.sub.E /2 at intermediate time of T.sub.E after applying 90.degree. pulse. Next, S.sub.1 scan to apply 180.degree. pulse is performed at time t=T.sub.E /2-.epsilon. earlier than T.sub.E by .epsilon. after 90.degree. pulse. The time obtaining the spin echo is t=T.sub.E in both S.sub.0 scan and S.sub.1 scan.
In this case, above-mentioned satisfies following formula. EQU .epsilon.=(4.multidot..sigma..multidot.f).sup.-1 ( 1)
.sigma.: chemical shift quantity of water and fat PA0 f: resonant frequency of proton PA0 .epsilon. corresponds to phase deviation period of magnetization vector of fat with respect to water, i.e., 1/4 of period 1/(.sigma..multidot.f) of chemical shift. Difference of the resonant frequency of proton in water and fat, i.e., the chemical shift .sigma. is about 3.5 ppm. Consequently, when the static magnetic field intensity is 0.5 T (Lamour frequency f=21.3 MHz in .sup.1 H), .epsilon. is about 3.5 msec.
FIGS. 5A and 5B are diagrams each representing the phase relation of the magnetization vectors of water and fat in S.sub.0 scan and S.sub.1 scan. In FIGS. 5A and 5B, W designates magnetization vector of water and F designates magnetization vector of fat, and X'-Y' coordinates are system of coordinates rotating about the Z axis at rotational speed of magnetization vector of water. In S.sub.0 scan of FIG. 5A, at t=0, i.e., at application of 90.degree. pulse, phases of both vectors are coincident. At t=T.sub.E /2, phase deviation .psi. (-.pi.&lt;.psi..ltoreq..pi.) of magnetization vectors of water and fat is produced due to chemical shift. Phases of both vectors are inverted about Y' axis by 180.degree. pulse from the Y'-axis direction. And then the magnetization vector of fat is rotated by the same amount as that before application of 180.degree.. pulse, and is coincident to the magnetization vector of water in phase at t=T.sub.E. In S.sub.1 scan of FIG. 5B, 180.degree. pulse is applied at t=T.sub.E /2-.epsilon.. This is earlier than the S.sub.0 scan by .epsilon. in time and by .pi./2 in angle of phase deviation. Time from the phase inversion by 180.degree. pulse until obtaining the spin echo is longer than time from 90.degree. pulse to 180.degree. pulse by 2.epsilon.. Since the magnetization vector of fat is rotated excessively corresponding to this, the phase deviation of 80.degree. is produced in the magnetization vectors of water and fat at t=T.sub.E.
Next, method of signal processing to obtain a separation image from raw data obtained in such manner will be described. Image data by image reconstruction of the raw data obtained by each scan becomes EQU S.sub.0 =W+F (2) EQU S.sub.1 =W-F (3)
Where W (.gtoreq.0) is proton density of water, and F (.gtoreq.0) is proton density of fat. Consequently, EQU W=(S.sub.0 +S.sub.1)/2 (4) EQU F=(S.sub.0 -S.sub.1)/2 (5)
are calculated per each pixel of matrix of the reconstruction image data thereby image in separation of water and fat can be obtained.
In each scan data, however, since there are 0-degree phase offset being proper to the apparatus and produced in the receiving system or the like and deviation of the center frequency of RF pulse included in the S.sub.1 scan data from the Lamour frequency and deviation of phase due to unevenness of the static magnetic field or the like, the actual image data becomes as following formulas. EQU S.sub.0 =(W+F) EXP(i.alpha..sub.0) (6) EQU S.sub.1 =(W-F) EXP{i(.alpha..sub.0 +2.theta.)} (7)
Where i.sup.2 =-1, and EXP(i.alpha..sub.0) is phase offset component being proper to the apparatus and EXP(i2.theta.) is phase deviation component due to unevenness of the static magnetic field and included in S.sub.1 data only. If such phase deviation component exists, separation of formulas (4), (5) cannot be performed well, but separation error of water and fat such as shading is produced. Consequently in the prior art, uneven distribution EXP(i.theta.) of the static magnetic field is previously measured using uniform water phantom, and the phase deviation component of the S.sub.1 scan is removed and corrected using this information. In another method, absolute value images of the image data of S.sub.0 and S.sub.1, EQU .vertline.S.sub.0 .vertline.=(S.sub.0 .times.S.sub.0 *).sup.1/2 W+F (8) EQU .vertline.S.sub.1 .vertline.=(S.sub.1 .times.S.sub.1 *).sup.1/2 =.vertline.W-F.vertline. (9)
are taken, and the phase deviation component is removed and then the separation image of water and fat using this absolute value data.
However, the above-mentioned correction methods have problems as follows. First, in the method using water phantom, on account of variation of permeability and antimagnetic field or the like due to difference of water and a human body in constituent components, the magnetic field distribution state is different at the phantom measuring state and at the photographing state of an article to be inspected. Consequently, exact correction cannot be performed and the separation error cannot be removed completely. Also when range of the phase deviation exceeds .+-..pi., the phase jump is produced and the correction becomes difficult resulting in another limitation. Next, in the method using the absolute value image, on account of .vertline.W-F.vertline., information is lost as to which of water or fat is more. Consequently, the calculation result of 1/2 of sum and difference of formulas (8) and (9) cannot perform identification as to which is water and which is fat, and it lacks the quantitativeness.